Question

Find the equation (in terms of x ) of the line through the points (-2,4) and (1,-5)y=

Answer 1

To determine the equation of a line that passes through (x₁,y₁) you can use the following formula:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).$

Substituting the given points in the above formula, you get:

$y-4=\frac{4-(-5)}{-2-1}(x-(-2)).$

Simplifying you get:

$\begin{gathered} y-4=\frac{9}{-3}(x+2), \\ y-4=-3(x+2). \end{gathered}$

Taking the above solution to its slope-intercept form, you get:

$\begin{gathered} y=-3x-6+4, \\ y=-3x-2. \end{gathered}$

Answer:

$y=-3x-2.$